RT info:eu-repo/semantics/article T1 Topologies of continuity for Carathéodory delay differential equations with applications in non-autonomous dynamics A1 Longo, Iacopo Paolo A1 Novo, Sylvia A1 Obaya, Rafael K1 Carathéodory functions, non-autonomous Carathéodory differential equations, continuous dependence on initial data, linearized skew-product semiflow. AB We study some already introduced and some new strong and weak topologies of integral type to provide continuous dependence on continuous initial data for the solutions of non-autonomous Carathéodory delay differential equations. As a consequence, we obtain new families of continuous skew-product semiflows generated by delay differential equations whose vector fields belong to such metric topological vector spaces of Lipschitz Carathéodory functions. Sufficient conditions for the equivalence of all or some of the considered strong or weak topologies are also given. Finally, we also provide results of continuous dependence of the solutions as well as of continuity of the skew-product semiflows generated by Carathéodory delay differential equations when the considered phase space is a Sobolev space. PB American Institute of Mathematical Sciences SN 1553-5231 YR 2019 FD 2019 LK http://uvadoc.uva.es/handle/10324/40204 UL http://uvadoc.uva.es/handle/10324/40204 LA eng NO Discrete and Continuous Dynamical Systems, 2019, vol. 39, no. 9, p. 5491-5520 NO Producción Científica DS UVaDOC RD 29-mar-2024